Electromagnetic Simulation of No-Insulation Coils Using H – $\phi$ Thin Shell Approximation

Abstract

When simulating no-insulation high-temperature superconducting pancake coils with the finite element (FE) method, the high aspect ratio of the thin turn-to-turn contact layer (T2TCL) leads to unfavorable meshes in these thin layers as manifested by a high number of degrees of freedom (DoF) or mesh elements of poor quality which decrease the accuracy of the simulation results. To mitigate this issue, we propose to collapse the T2TCL volume into a surface using a thin shell approximation (TSA) for three-dimensional FE analysis. A ⃗ H − ϕ formulation is used and solves for the magnetic field strength ⃗ H in conducting domains and the magnetic scalar potential ϕ in insulating domains. This formulation avoids spurious currents and reduces the number of DoF in insulating domains. Automatically created thick cuts are used to deal with multiply connected domains. Particular attention is paid to the interpretation of these cuts and the corresponding basis functions in the context of pancake coil geometries.The efficiency of the formulation facilitates the resolution of each turn. In this way, local phenomena such as quench can be captured in a straightforward way. The TSA formulation is verified by comparison against a reference model with volumetrically meshed T2TCL and is shown to be accurate and efficient, significantly reducing the solution time while reducing the effort for creating high-quality meshes. The TSA is implemented in an open-source FE framework and the source code is shared alongside this paper.

An open-source 3D FE quench simulation tool for no-insulation HTS pancake coils

“…magnetodynamic simulations [22], and coupled magnetothermal simulations [24]. With the thin-shell approximation, the radial currents flowing across contact layers are also captured, and the results are in good agreement with simulations that use 3D contact layers [22].…”

“…FiQuS/Pancake3D is capable of conducting both magnetodynamic and coupled magneto-thermal simulations. For magnetodynamics, it uses an ⃗ H − ϕ formulation in the whole computational domain, Ω, with details in [22]. This formulation is an efficient and robust choice for systems of HTS without ferromagnetic materials [23].…”

Study of the demagnetization behavior of no-insulation persistent-current mode HTS coils under external AC fields by 3D FEM simulation

“…For finite-element method (FEM) models, Zhao et al [52] and Wang et al [53] proposed 3D models that built all the distinct HTS tapes including the specific turn-to-turn-contact and superconducting layers. Schnaubelt et al [54] built an NI HTS coil model based on the H−ϕ formulation with the turn-to-turn contact layers modeled as the shell elements. Mataira et al [55][56][57] proposed a method that models the NI coil as a homogeneous bulk set with an anisotropic resistivity; this method has been used and verified by quite a few groups in the world [58][59][60][61][62][63][64][65].…”

Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils

“…First, a thermal TSA to represent thin insulation layers by considering the heat equation was introduced in [14]. Second, a magnetodynamic ⃗ H − ϕ TSA was used to study the charge and discharge of NI coils in [16]. By replacing T2TCL volumes with surfaces, no volumetric mesh of the thin layer is required.…”

“…By replacing T2TCL volumes with surfaces, no volumetric mesh of the thin layer is required. This work proposes to combine the thermal TSA of [14] and the magnetodynamic TSA of [16] to model T2TCL with magneto-thermal T2TCL taking into account the coupling via i) non-linear material relations and ii) Joule losses.…”